Saturday, December 1, 2012

So I read DeLong as arguing Nagel is wrong because he thinks reason gives us some kind of transcendental access to objective truth. He writes (paraphrasing Nagel): "My mind is in immediate contact with the rational order of the universe!... I abandon the belief that I am going south-southwest because my reason's transcendent grasp of objective reality makes me know with certainty that it could not possibly be true!"

It is the foundationalism of Nagel's approach to reason that bothers DeLong, not the mere fact that he used reason!

Landsburg doesn't address this criticism at all. He simply notes that we reason about things that we have no empirical access to (unlike the sun rising, which we reason about and then observe). He provides a list:

"1) The ratio of the circumference of a (euclidean) circle to its radius is greater than 6.28 but less than 6.29.2) Every natural number can be uniquely factored into primes.3) Every natural number is the sum of four squares.4) Zorn’s Lemma is equivalent to the Axiom of Choice (given the other axioms of Zermelo-Frankel set theory).5) The realization of a normally distributed random variable has probability greater than .95, but less than .96, of lying within two standard deviations of the mean..."

And then gives us five more along the same lines.

Right to all of them (I'm trusting Landsburg on Zorn and a few others I don't know myself). Landsburg shows we reason abstractly too.

So? What's his point exactly? Does he think Brad DeLong doesn't think we reason abstractly? Or that reason is useless? I guess that's what Landsburg is arguing, but I've never seen Brad say anything like that.

And what does Landsburg think of the claim that this list is just a set of results that we get out of applying the rules of word games that we've developed? They are "right" and "true" in the context of the logic of that word play (the rules of mathematics that we set up, etc.) but not in any objective sense outside of that word play. Except, of course, insofar as that word play seems very useful for describing the universe, whether you're a physicist or an economist. But once we get into description of the universe, of course, we move into the territory of our frail faculties (as if some of our mathematical brains weren't frail enough!) and we are still not connecting to any "objective" or "transcendent" reality.

30 comments:

But the truths of arithmetic are provably *not* "just a set of results that we get out of applying the rules of word games we've developed". (Is the statement "the North won the Civil War" just a result that we get out of applying the rules of word games we've developed? If not, why not, and why doesn't your argument apply also to arithmetic?)

Nor is mathematics (or, more concretely arithmetic) anything like an "internally consistent logical structure" --- assuming that you are using the phrase "logical structure" in anything like its usual sense (a recursive set of axioms, a recursive set of rules of inference, etc).

You might or might not have a point buried here, but saying silly things like "mathematics is a logical structure" leads one to suspect that you haven't actually thought about any of this very hard.

I was having trouble excavating your point too - this was just an attempt.

I'm not sure how mathematics is not an internally consistent logical structure, but let's grant your point that it's not.

You still miss Brad's point by a long shot. The problem is not with reasoning. Indeed he talks about using reasoning to great effect. The problem is with the foundationalist claim that reasoning gives you access to a transcendental or objective truth. That we can cobble together sentences that we consider "true" by the rules of mathematics is very much not the full extent of what Nagel seems to be claiming (I'll add again the disclaimer from my initial post that I don't know Nagel and I'm just adding my two cents conditional on everything everyone is claiming about Nagel being essentially right).

But the truths of arithmetic are provably *not* "just a set of results that we get out of applying the rules of word games we've developed". (Is the statement "the North won the Civil War" just a result that we get out of applying the rules of word games we've developed? If not, why not, and why doesn't your argument apply also to arithmetic?)

Nor is mathematics (or, more concretely arithmetic) anything like an "internally consistent logical structure" --- assuming that you are using the phrase "logical structure" in anything like its usual sense (a recursive set of axioms, a recursive set of rules of inference, etc).

You might or might not have a point buried here, but saying silly things like "mathematics is a logical structure" leads one to suspect that you haven't actually thought about any of this very hard.

Second, can you provide me with the premises that lead to the conclusion that I am "not connecting to any "objective" or "transcendent" reality"? Just a sketch of your argument, but with the premises laid out in the form(1)(2)(3)...C:

Because I take it that you, the person Daniel Kuehn, is also subject to the same limitations, I set the following constraint on your argument: you cannot rely on an premise that makes a claim about an objective reality outside yourself. Thanks.

If you are accessing something transcendent, your access is properly termed "transcendental". I don't know what your concern is exactly. I hope you're not confusing this with some kind of spiritualist/romantic claim. It's quite appropriate as used here as far as I can tell.

Why exactly aren't you letting me make a claim about an objective reality outside myself? There's a big difference, it seems to me, between noting that there's probably an objective reality out there and claiming that my experience with what seems to be that objective reality is itself objective. There's a big difference between the claim "there is no objective thing outside myself" (which I don't make) and the claim "we don't judge truth by correspondence with an objective reality" or "we don't have unmediated access to objective reality". The first claim seems ridiculous to me. The second and third strike me as common sensical.

I'm still working my way through my own beliefs re: epistemology and metaphysics. So dont take this as a motivated attack. I'm curious about all theories and you seem like a guy with pretty entrenched views on the subject, so I thought I would press you a little bit in areas I find difficult for pragmatists to square. This is what I am getting at. You have these two conclusions:C1: "we don't judge truth by correspondence with an objective reality";C2: "we don't have unmediated access to objective reality";C3: something like "we don't have delusions of 'objective truth'".

I would like to see the premises that lead to these conclusions, and I would like to restrict the scope of these premises in such a way that they do not rely on claims about how things really are. I do not think certain types of pragmatists can legitimately make reference to the way humans are, the type of being that a human is, or anything like this. For example, I believe that it is an objective truth that human beings are products of an evolutionary process. As a result, human beings have limited capacities. Therefore, human beings do not have the capacity to know everything or know what their limitations are. This may lead one towards a type of pragmatism. But the premise that leads me in that direction (belief in evolution) leads me quickly out of it. I believe that evolution is true--a fact about objective reality, something that humans have the capacity to know, and know directly. So once I keep this in mind, I cannot consistently believe that humans do not have the capacity to know of an objective reality--for the original belief that lead me down that road is a belief about objective truth.

I start becoming a little skeptical when you make claims about "we" do this or that, and "we" have the capacity for this or that. These seems to be claims about a reality outside yourself. But if "we" don't have access to objective reality, then "you" don't have access to anything "real" outside yourself. So I'm not sure why you feel comfortable making claims about "we".

Regarding "transcendental" and "transcendent". My familiarity with "transcendental" is as a type of philosophical argument of a certain form (e.g., some fact F is obviously true, x,y,z are necessary conditions for fact F to be true; therefore, x,y,z are necessarily true). "Transcendent", on the other hand, is something beyond our sense capacities. THe reason why I expressed concern, not a big deal though, is that from a historical standpoint, Kant invented the "transcendental" in order to show that traditional metaphysicians were speaking nonsense in their claims about "transcendent" reality. Because I view the transcendental as a certain form of argument, I'm not sure what it means to say one has special "transcendental access" to the transcendent.

So I'm not a philosopher, and I'm not sure I could come up with premise-conclusion arrangements. I probably could do something if I thought about, but it might not be convincing. You're probably better served by someone who finds these ideas convincing but is trained as a philosopher. I'm a social scientist. I spend all my time thinking about human behavior, but not necessarily about philosophy. Obviously there's an overlap when we're talking about the way humans interact with the world around them.

I think the way that you start with a sort of fallibilism by talking about that "type of pragmatism" that follows from evolution. That's no coincidence of course. Darwin fueled a lot of the early pragmatists. It's also nice because you don't have to be a pragmatist to accept fallibilism. Few people don't have a at least a bit of that in them.

You seem to want to say that any sense of certainty is unpragmatic. I don't know what pragmatic philosophers have to say about that, but my strong impression is that that's not a view they'd take. You are certain we evolved from other organisms who really didn't have the same sort of cognitive capacity we do. I agree. You believe so strongly in it you call it "objective truth", a "fact". In a discussion that isn't explicitly about pragmatism I'd use those words too.

But why are you so certain about evolution?

I am certain about evolution because it seems to explain everything I see in the world. It's an organizing idea that makes sense of my surroundings. It seems plausible too. And a lot of people a lot smarter than me seem to agree on that. And - to get a little feisty - a lot of the people that disagree seem a lot less smart than me. So that all tells me at least two things about evolution:

1. It's something I can be really certain of, and2. Its value is entirely contingent on (a.) my interaction with other things, (b.) my limited experiences with other things, (c.) other people's interaction with other things, (d.) other peoples' limited experiences with other things, and (e.) my ability to assess other people (e.g. - if creationists are actually getting their information from revelation from an actual omniscient being I'm in real trouble with my theory).

I call it "objective truth" as short hand, of course. I'm so comfortable going through my life treating it like "true reality" and I've grown up in a culture that has sprung forth from Plato that I have a hard time not calling it "objective truth" in casual conversation.

re: "I start becoming a little skeptical when you make claims about "we" do this or that, and "we" have the capacity for this or that. These seems to be claims about a reality outside yourself. But if "we" don't have access to objective reality, then "you" don't have access to anything "real" outside yourself. So I'm not sure why you feel comfortable making claims about "we"."

Gene made comments like this the other day.

Right, it's a good guess which is all I can do.

Gene didn't like my use of the word "know". His critique was very strange in my view. He took his quite non-pragmatic epistemology and decided that that was exactly what "know" meant all the time. So when I said that I "know" something I was clearly contradicting myself.

Of course not. "Know" to me has different implications because I have a different epistemology. Rorty said that the word "truth" is the compliment we pay to sentences that pay their way. You can't assume pragmatism is wrong, define all words on the assumption that it's wrong, and then criticize pragmatists who use the words because they think the words imply something somewhat different.

I really am not a philosopher. I was not aware of everything Kant has said on the matter.

As a social scientist interested in human relations to each other and their world, I'm going to be talking about things that a lot of philosophers are also interested in.

And in my vague sense of philosophy (I'm not entirely unread - just largely unread) there are definitely well regarded viewpoints that seem to get at things better than other well regarded viewpoints. But I definitely will always talk on here like an informed, interested social scientist.

The trouble is we both "own" these issues. As a citizen and a social scientist I have business talking about democracy (our usual friction point!). As a citizen and a philosopher you have business talking about democracy. We will often talk about it in very different ways. I often won't be able to keep up. I think the trick is patience, methodological pluralism, and continued interest. I really do enjoy your comments on here. You're not always going to be able to convince me that because I can't defend my views like a philosopher would defend my views that I don't have grounds to hold those views ;-)

*sigh* Daniel, DeLong is totally wrong on this, but Steve is being coy with you here for some reason. I.e. I think Steve's 10 statements blow up DeLong's blog post, but unfortunately I also understand why you aren't seeing it, even after Steve has chimed in here.

I don't know if Landsburg is being coy. His post is perfectly intelligible. I think he's thinking that Brad is claiming something really outlandish.

You seemed to think he was saying something deep about Kant. Enough smart people have concerns about all that that I don't think listing math problems "blows up" anything. I'm sure Gordon has some interesting things to say, though, and I'll try to get a chance to listen to him.

Otherwise I'm not sure what to make of this... *sigh* I guess I'll just have to wait for your post.

I actually agree that it's possible I've totally missed DeLong's point. He apparently thought his point was so obvious that there was no need to spell it out. I sometimes make the same mistake.

I do contend that pure reason is capable of revealing objective truths, which seems to me to conflict with what DeLong *seemed* to say, but might or might not conflict with he *meant* to say.

And, more to the immediate point, I repeat that anyone who characterizes arithmetic as a "logical system" is almost surely too ignorant to say anything useful on this subject. (Note: "Ignorant" is not a pejorative. I myself am too ignorant to say anything useful on 99% of all subjects; so are you. It just so happens that this particular subject is in my 1% but apparently not in yours.)

I'd really appreciate at least a brief discussion of what you mean instead of continuing to tell me that I'm not making a contribution here.

I suspect you've invested a lot into the phrase "logical structure" because of the way you've used it formally in the past - for example some of what you've discussed about numbers. I suspect that because of the subject at hand here, but of course I have no clue if that's the case because you're not elaborating.

Your use of that phrase in that context is of course not how it's always used all the time. If you can't help but read it that way, perhaps I could substitute something far more general like "rule-based ways of talking about abstract ideas that help us think productively about the world around us" for "logical structure".

Maybe you'd have a problem with that too. I really couldn't say because you are not elaborating on what your concerns are.

I hope this all doesn't boil down to the idea that if you don't think numbers are ontologically primary you don't have the chops to talk about anything that references logic or numbers or anything else.

But again - it's hard for me to say if that's what it boils down to because I really don't know exactly what your concerns are here.

I'm only somewhat familiar with what you've said about the ontological primacy of numbers. I haven't read your book, but this little exchange is going to motivate me to look at that section in The Big Questions potentially.

What I've read on your blog seems very impressionistic to me, but I'm sure what's on the blog is relatively abbreviated.

I don't see any warrant to jump into Platonism over it. I don't see anything immediately wrong about thinking about numbers as useful ways of talking about regularities in the world. But I'm not a philosopher of mathematics. Just because I'm not a philosopher of mathematics, though, does not mean that I find your take on it on the blog that I've read particularly plausible.

Here's a thought: maybe Platonists are predisposed to thinking about the philosophy of mathematics? Could that be relevant at all?

I hope this all doesn't boil down to the idea that if you don't think numbers are ontologically primary you don't have the chops to talk about anything that references logic or numbers or anything else.

Of course it doesn't. It boils down to this:

perhaps I could substitute something far more general like "rule-based ways of talking about abstract ideas that help us think productively about the world around us" for "logical structure".

The idea of a squirrel is an abstraction. There are rule-based ways of talking about squirrels that help us think productively about the world around us. Do you want to call a squirrel a "logical structure"? If not, you're being inconsistent. If so, I think your notion of "logical structure" is far too broad to be remotely helpful.

I call the way we approach taxonomy or more specifically, just naming things squirrels - a rule based way of talking about reality that help us order our thoughts.

This idea of a squirrel is an abstraction that's given meaning by this rule-based structure for thinking that we've concocted.

The brown furry thing running around my yard is not an abstraction of course. But we use taxonomy to talk productively about it.

The regularities and magnitudes in the universe are not abstractions. But we use math and arithmetic to talk productively about them. Sometimes we even slip into Platonism because that's a convenient way of talking about it all too. But talking in that way doesn't make any of the abstractions "real".

PS: Arithmetic is not a logical structure for the same reason it's not a geometric structure --- logic, geometry and arithmetic are all different branches of mathematics. If you're going to redefine logic so that it encompasses all of mathematics, you might as well do the same with geometry and call arithmetic a "geometric structure". What would that gain you, other than ease of obfuscation?

When a pair of these pairs come together there's always the same amount of them: four.

We've come up with a rule based way of talking about this sort of thing: arithmetic. It turns out to be tremendously useful. Whenever there is one of a thing and another that is like that thing but not that thing and I think about them together I can name that "two of those things". When I get two of two of those things I always call that "four of those things". Whenever two of two of those things are around I always seem to have the same number of similar-but-not-the-same things: One, and then another, and then another, and then another. It never turns out differently.

Arithmetic is a great way talking about all this in a structured way.

If "two" has any kind of ontological significance on its own, rather than being a nice way of talking about one thing that is like another thing but not the other thing, that ontological significance has escaped me. I don't see any reason to think it couldn't have ontological significance but I don't see any reason to assume it does either.

Regarding your PS - that's why I rephrased it. I got the impression you were thinking in terms of formal logic.

Lots of people use the word "logic" besides mathematicians.

I'm not redefining "logic" any more than my wife is redefining "rational" when she uses it to mean something other than transitive and complete preference orderings. When people use "rational" in a way that's different from how economists use it, you don't go around claiming that they are obfuscating don't you?

What do you gain by dragging this out for several comments without clarifying what your problem even is, without obfuscating?

This is not a mathematics blog. Words ought to be read in the proper context.

But if you've still got an issue with it, that's why I offered an alternative. But I'm not going to concede to having redefined anything.

1) You keep raising the issue of ontology. Ontology has nothing to do with this. You can be a pure platonist, or you can believe that arithmetic is a purely human invention, or anything else you want to believe, but it's got nothing to do with the point at hand.

2) You are free to use the word "logic" in any informal sense that you want to use it in. But in the sense in which seem to be using the word, a squirrel is neither more nor less a "logical structure" than arithmetic is. If you are using the phrase "logical structure" in a way that makes *everything* a logical structure, then I don't see what it adds to the discussion. If you are using it in some other way, perhaps you'd like to spell out what that other way is, because I can't begin to guess what it might be.

3) You said that the items on my list were just "the result of applying the rules of word games". Under the obvious interpretation (where "rules of word games" means logic, in its formal sense), this is provably false. Under the second-most-obvious interpretation (where "rules of word games" means anything we're capable of talking about), your description applies equally well to the facts of biology and history, and therefore seems to be so broad as to add no enlightenment to the discussion. What DID you mean? More specifically: Are you or are you not using the phrase "rules of word games" in a way that would apply equally well to the statement that the North won the Civil War?

On the ontology of numbers, you need to understand that I haven't been sure what does and doesn't have to do with this because until about an hour ago you weren't furnishing details on what your concerns were. I didn't have much to go on except what you've said about 2 + 2 = 4 (or, alternatively "two plus two equals four") in the past.

On logical structures I gave you an alternative. Is there a concern about that? You are the only one that seems to be concerned about this point, so I tend to think it's working fine and you are reading a lot more into it than you need to.

To a certain extent any language with any grammar to speak of could fall under this definition. It seems useful of course to think specifically of more methodical thought. But that's not necessary. It can mean "anything we're capable of thinking", because when we think about the world around us we are organizing experiences using concepts and rules that relate concepts to other concepts.

That makes a big difference in how we think about the world around us.

The way we've come up with concepts (like "squirrel" to describe a whole group of furry brown things, but not other furry brown things) and rules to relate those concepts is critical to how we interact with and think about things outside ourselves.

If a description of how we interact with and think about things outside ourselves doesn't enlighten a discussion about whether or not we are grasping an "objective" reality, I don't know what does.

If you need more clarification on what I "mean" I may have to throw in the towel. I'm running out of ways to put this, Steve.

"My mind is in immediate contact with the rational order of the universe!... I abandon the belief that I am going south-southwest because my reason's transcendent grasp of objective reality makes me know with certainty that it could not possibly be true!"

As I have shown, this is a TERRIBLE misreading of what Nagel wrote. Of course, when I made just a passing remark about DeLong, he linked to it and jumped all over it. So I followed up and showed his version of Nagel is a complete straw man. THAT post he completely ignored.

"I'm just adding my two cents conditional on everything everyone is claiming about Nagel being essentially right"

That is a very strange conditional, since I have very pointedly argued that DeLong got Nagel ludicrously wrong.

I really am not interested in hashing out Nagel. On the plus side, I'm not endorsing Brad's view of Nagel at all.

It's not a strange conditional, I don't think. Maybe I should have said this: I don't know if that's what Nagel thinks and I don't particularly care. Let's say Person X thinks what Brad claims Nagel thinks. Taking that as a conversation starter, I want to concur with a lot of the points that Brad is making.

Is that better perhaps? I don't want to be seen as saying that I'm giving DeLong's Nagel the benefit of the doubt. I really can't arbitrate that one and am not interested in arbitrating that one.

Steve, in case you're still reading this: I think your blog post was superb, except for the stuff about Dirac at the end where (in my opinion) you overstated your case and will allow DeLong to dismiss your whole post.

What made me *sigh* here is that you are being cryptic in these comments (not in your original post) with Daniel. *I* don't even know what you mean when you keep chastising him about math. Presumably you're not saying it's illogical, or that it doesn't have a structure, right? But I'm afraid to speak up more and fall into the 99%. :)

Steve, do you just object to "logical structure" in the same way you'd object if I described an oak tree in my front lawn as a logical structure? I.e. you think this characterization plays into this very dispute, where Daniel thinks math is just some handy dandy convention we invented, versus something deeply embedded in the nature of reality that we discover through thought?

Bob: A "logical structure" should consist (roughly) of: a) A set of symbols, b) some grammatical rules for combining these symbols into things called "sentences", c) a recursive list of sentences that are designated "axioms" (here "recursive" means "comprehensible to a computer"), d) a recursive list of rules of inference that allow you, given a list of sentences, to write down other sentences that are declared to be "deducible" from the sentences on the list.

An oak tree is not a logical structure, becuause an oak tree is not a set of symbols, or a set of grammatical rules, or a list of axioms, or a list of rules of inference, or any combination thereof. The natural numbers are not a logical structure for exactly the same reason.

A hundred years ago, it was reasonable to hope that there might be a logical structure that in some sense "encodes" the natural numbers, so that in some extremely rough and imprecise sense, the natural numbers could be thought of as somehow being like that logical structure. Given theorems of Godel, Lowenheim-Skolem, Tarski, etc, that have been around for a century or so, there is now known to be no hope of anything of the kind.

Suppose someone comes to you with an idea about economics, and embedded somewhere in his presentation is the phrase "And of course, economic theory tells us that the only way to maintain a stable price level is to use cows for money." You reply, with as much respect as you can muster, that a person capable of saying such a thing is probably not a person who has thought very hard about economics. This person then asks you to elaborate on your objection. You reply that, well, it's simply NOT TRUE that economic theory tells us that the only way to maintain a stable price level is to use cows for money, and that moreover you can't imagine what would ever lead a person to believe such a thing. This person then accuses you of being coy and unspecific abot your objections.